WASHINGTON -- The steep rise in coronavirus deaths appeared to be leveling off Monday in hard-hit New York, echoing a trend underway in Italy and Spain, while the crisis escalated alarmingly in Britain, where Prime Minister Boris Johnson was moved to intensive care after his condition deteriorated.

Johnson, 55, was conscious and did not immediately need to be put on a ventilator, his office said. The prime minister is the world's first known head of government to fall ill with the virus.

U.S. President Donald Trump said he asked "leading companies" to contact officials in London about therapies that could help Johnson, calling them complex treatments that have been recently developed by the unnamed companies.

"We have contacted all of Boris' doctors, and we'll see what's going to take place, but they are ready to go," Trump told reporters.

Trump said U.S. mitigation efforts are showing signs of slowing the spread of the virus. The government is distributing millions of N95 respirators, masks, face shields, gowns and gloves, the president said, without specifying where the equipment is going.

In the hot spot of New York, Gov. Andrew Cuomo announced the first, faint signs the outbreak there might be at or near its peak, while warning it's no time to relax social distancing restrictions. He ordered bigger fines against violators.

"The numbers look like it may be turning. 'Yay, it's over!' No, it's not. And other places have made that mistake," he said as deaths in the U.S. climbed past 10,000, with around 350,000 confirmed infections.

President Donald Trump describes a call with presidential candidate Joe Biden about the coronavirus pandemic.

Stocks rallied on Wall Street and around the world on the news out of the U.S. and places like Italy and Spain. The Dow Jones Industrial Average gained more than 1,600 points, or nearly 8%.

Outbreaks in other places moved in the opposite direction: France recorded its highest 24-hour death toll since the epidemic began, 833. And Japan considered a state of emergency for Tokyo and other areas because of soaring infections in the country with the world's third-largest economy and its oldest population.

Worldwide, more than 1.3 million people have been confirmed infected and over 74,000 have died, according to Johns Hopkins University. The true numbers are certainly much higher, because of limited testing, different ways nations count the dead and deliberate under-reporting by some governments.

The latest data suggests that social distancing appears to be working in some countries, and better than expected.

One of the main models on the outbreak, the University of Washington's, is now projecting about 82,000 U.S. deaths through early August, or 12 percent fewer than previously forecast, with the highest number of daily deaths occurring April 16. The model relies on much more robust data from Italy and Spain and from hospitals.

The number of dead in New York state rose past 4,700, and the death toll in New York City closed in on the 2,753 lives lost at the World Trade Center on 9/11.

The state has been averaging just under 600 deaths per day for the past four days. Though horrific, the roughly steady daily totals were seen as a positive sign. Cuomo also reported that the number of new people entering hospitals daily has dropped, as has the number of critically ill patients who require ventilators.

At the same time, he ordered schools and nonessential businesses to remain closed until the end of the month, announced he is doubling the fines for rule breakers to $1,000. He also warned that hospitals are under extreme pressure.

To help ease the strain, a military hospital ship that was sent to New York City can now accept COVID-19 patients, Trump said. Cuomo tweeted that the USNS Comfort would add 1,000 beds staffed by federal personnel, providing "much-needed relief."

Globally, Austria and the Czech Republic began discussing how to ease some of the crippling restrictions, starting with reopening some small shops and garden centers next week.

Deaths in Britain climbed by more than 400 Monday, for a total of nearly 5,400. Sunday was especially bleak, with more than 600 deaths - more than Italy recorded.

Italy's day-to-day count of new COVID-19 cases dipped again, for the smallest one-day increase in early three weeks. The country, ravaged by the virus, also saw a drop for the third straight day in intensive care beds occupied by infected patients.

Premier Giuseppe Conte promised Italians that they will soon "reap the fruit of these sacrifices" in personal liberties, though he declined to say when the lockdown would be lifted.

Italy has the world's highest death toll - over 16,500 - but the pressure on intensive care units in the north has eased so much that it's no longer airlifting patients to other regions.

Nursing coordinator Maria Berardelli at the hard-hit Pope John XXIII hospital in Bergamo said that while the numbers of new patients had eased a bit, hospital staffers were still pulling long, difficult shifts.

"There has been no reduction in the work," Berardelli said. "There have been fewer admissions to the emergency room, but our intensive care units are still full, so the activity hasn't been reduced."

In Spain, deaths and new infections dropped again. The health ministry reported 637 new deaths, the lowest toll in 13 days, for a total of over 13,000 dead. New infections were also the lowest in two weeks.

Emergency rooms in the hard-hit Madrid region of 6.6 million were returning almost to normal a week after scenes of patients sleeping on floors and in chairs.

Transport, Mobility and Urban Affairs Minister José Luis Ábalos said the figures show Spain is entering "a new phase of the battle."

"This new phase does not mean we can let down our guard. We are assessing the measures that we will need to adopt," Ábalos said.

It was a message repeated worldwide: Any gains could easily be reversed if people do not continue to abide by lockdown rules.

A report from a federal watchdog agency found that three out of four U.S. hospitals surveyed are already treating patients with confirmed or suspected COVID-19. And some places, like Maryland, Virginia and Washington, D.C., are predicting the peak won't come until May or well into the summer.

Baton Rouge, Louisiana, reported the death of a girl born prematurely after her mother contracted the disease and was put on a ventilator. Louisiana, where millions of tourists visit New Orleans yearly, had over 500 deaths.

However, Gov. John Bel Edwards says the state's death and hospital admission rates could suggest infections are slowing.

"We are starting to see real signs that these mitigation measures that we put into place weeks ago are starting to bear real results," he said.

The virus is spread by droplets from coughs or sneezes. For most people, the virus causes mild to moderate symptoms such as fever and cough. But for some, especially older adults and the infirm, it can cause pneumonia. Over 270,000 people have recovered worldwide.